To help settle an office discussion could someone please explain why this is/is not possible.

Assuming that materials could be found that are light and strong enough for its construction.

If you were to feed the back-end of a wind tunnel to the front forming a torus and circulating the air back around could you then place a wing in the this tunnel and produce enough lift to fly the torus?

Is the point i having a torus with air circulating inside the torus and wings also inside the torus? No, It's impossible. It's like to lift yourself by pushing your head upwards. As one of three basic sentences of physics says: Every force induce reaction force with same value and opposite direction. Your force is lift of the wing, reaction force is force pushing the air downwards and the torus with it.
–
CrowleyJun 15 '11 at 11:01

3 Answers
3

No. Concerning aerodynamic forces, the wind tunnel is a closed system (I.e. no exchange of momentum with the outside is possible), so it won't move.
Crowley's comment is an alternative and equally valid formulation/argument.

To understand why, mentally draw a freebody diagram of the system in space. You have a torus. You do not know (or care) what is inside the torus. The torus is motionless. Now someone starts a process inside the torus (again, you do not know, nor care, what). That process is allowed to continue to its end (or some steady state). Nothing leaves nor enters the system during this time.

The end result, per the law of conservation of momentum, is that the center of mass of this system has not moved. Also, per Newtons law of F=ma, since the outside forces acting upon this system sum to zero, we must assume 'a' is zero; therfore the center of the mass of the system did not move.

Actually, if the wing was tethered to the floor of the torus, the wing could 'kite'. The lift is produced by air flow over the wing. As long as there is a tether to counter the drag produced, the wing will lift in proportion to the air speed. Without the tether, drag and gravity would pull the wing backward and to the floor. In short, you need something to counter the drag, either some form of thrust or a tether to be able to generate lift.

Another possibility is to tilt the torus to some angle steeper than the lift to drag ratio of the wing. Then the wing could theoretically soar the rising air in one side of the torus.

By the way, a convection cycle is like a torus. You have air heated by the sun which rises, the vacated space is filled with sinking cooler air. Soaring gliders ride these vertical currents for hours.